# Untitled

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```class Program
{
const int N = 8;

static void Main(string[] args)
{
int count = 0;
int[,] board = new int[N, N];

//Initialize the board array to 0
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
board[i, j] = 0;
}
}

//Initialize the pointer array
int[] pointer = new int[N];
for (int i = 0; i < N; i++)
{
pointer[i] = -1;
}

//Implementation of Back Tracking Algorithm
for (int j = 0; ;)
{
pointer[j]++;

//Reset and move one column back
if (pointer[j] == N)
{
board[pointer[j] - 1, j] = 0;
pointer[j] = -1;
j--;

if (j == -1)
{
Console.WriteLine("all possible solutions to N–Queens problem are done");
break;
}
}
else
{
board[pointer[j], j] = 1;
if (pointer[j] != 0)
{
board[pointer[j] - 1, j] = 0;
}

if (SolutionCheck(board))
{
j++;//move to next column

if (j == N)
{
j--;
count++;
Console.WriteLine("Solution" + count.ToString() + ":");
for (int p = 0; p < N; p++)
{
for (int q = 0; q < N; q++)
{
Console.Write(board[p, q] + " ");
}
Console.WriteLine();
}
}
}
}
}

}

public static bool SolutionCheck(int[,] board)
{
//Row check
for (int i = 0; i < N; i++)
{
int sum = 0;
for (int j = 0; j < N; j++)
{
sum = sum + board[i, j];
}

if (sum > 1)
{
return false;
}
}

//Main diagonal check
//above
for (int i = 0, j = N - 2; j >= 0; j--)
{
int sum = 0;
for (int p = i, q = j; q < N; p++, q++)
{
sum = sum + board[p, q];
}

if (sum > 1)
{
return false;
}
}

//below
for (int i = 1, j = 0; i < N - 1; i++)
{
int sum = 0;
for (int p = i, q = j; p < N; p++, q++)
{
sum = sum + board[p, q];
}

if (sum > 1)
{
return false;
}
}

//Minor diagonal check
//above
for (int i = 0, j = 1; j < N; j++)
{
int sum = 0;
for (int p = i, q = j; q >= 0; p++, q--)
{
sum = sum + board[p, q];
}

if (sum > 1)
{
return false;
}
}

//below
for (int i = 1, j = N - 1; i < N - 1; i++)
{
int sum = 0;
for (int p = i, q = j; p < N; p++, q--)
{
sum = sum + board[p, q];
}

if (sum > 1)
{
return false;
}
}
return true;
}

}```